We investigate the performance of a numerical model based on fully nonlinear depth-averaged equations for simulating wave propagation, transformation and overtopping over coastal structures. The model is based on the weakly-dispersive Serre-Green-Naghdi equations, solved with a high-order finite-volume/finite-difference scheme. Wave breaking is modelled either by locally switching to the nonlinear shallow water equations or by adding a diffusive-like term to dissipate energy, with a turbulent viscosity computed from the turbulent kinetic energy. Contrary to the former approach, the latter allows to perform computations with fine meshes, which is necessary to compute wave run-up and overtopping accurately. The model is used to reproduce experiments of solitary and irregular wave propagation, breaking, run-up and overtopping, with satisfactory results.

Accurate hindcasting of sea state events is a cornerstone of coastal engineering, risk assessment, and climate-related studies, yet it remains limited by uncertainties in physical parameterizations and model structure. This study introduces an automated calibration framework based on Bayesian Optimization (BO) using the Tree-structured Parzen Estimator (TPE) to constrain key dissipative processes in the ANEMOC-3 hindcast wave model, including bottom-friction losses, depth-induced wave breaking, and dissipation driven by wave strong opposing currents. The methodology enables the joint optimization of continuous physical parameters and discrete model structure choices within a unified probabilistic search space, significantly reducing model-observation misfit. Calibration is conducted over the high energy storm conditions of February 2014, while transferability is assessed both temporally and spatially, through independent validation on January 2014 and January 2018 events and across a network of offshore and coastal buoy observations. The optimized configurations retain skill beyond the calibration period and across observation sites, yielding systematically improved agreement with buoy measurements in terms of bias, root mean square error, and scatter index relative to the reference configuration. These results highlight the potential of Bayesian Optimization as a scalable and robust framework for automating the calibration of complex wave hindcast systems. Future developments will address multi-objective optimization, uncertainty quantification, and the integration of complementary observational datasets.

Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes simultaneously to all directions according to linear wave theory. Meanwhile, conventional compressed sensing methods based on ℓ_1-shrinkage tend to underestimate signal energy when sparsity is not strictly satisfied, leading to biased spectral estimation. This paper introduces a group sparsity constraint to promote physically consistent sparse representations across channels. An energy constraint is proposed in the form of a soft lower bound, enabling an isotropic rescaling of the recovered spectrum while preserving its sparse structure. Considering a large volume of buoy data, we demonstrate through a series of experiments that the proposed approach enables compression by retaining a subset of original measurements.

Admissible average overtopping discharges in given storm conditions are typically used to design coastal protections, in particular dykes or breakwaters. These discharges are usually estimated using semi-empirical formulas relying on wave conditions at the toe of the structure. These formulas, unfortunately, only work for simple configurations, invariant alongshore, and can be insufficient for complex sea states. Therefore, numerical modelling could be a more flexible alternative for estimating these discharges. This work presents the development and validation of a Boussinesq-type numerical model solving the fully-nonlinear weakly-dispersive enhanced Serre-Green-Naghdi equations for the simulation of random wave overtopping over impermeable structures in one horizontal dimension. Wave breaking is modelled with an eddy viscosity approach based on the turbulent kinetic energy, which is robust and accurate at describing energy dissipation in the surf zone. Two distinct experimental datasets, with 184 trials in total and very dissimilar wave conditions and foreshore seabed profiles, are used to validate the model regarding wave propagation, shoaling, breaking and overtopping. Both unimodal and bimodal sea states are considered. Average overtopping discharges in configurations with deep and very shallow foreshores, as well as for breaking and non-breaking waves, are well reproduced by the model. For instance, typical mean relative errors on the simulated mean overtopping rates are found to lie within +/- 20% compared with the measurements, at least for the largest discharges of the considered campaigns. The scatter of simulated discharges is somewhat higher for lower discharges, but the results remain in an acceptable range.

The study aims to demonstrate the capabilities of a CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) to predict wave-structure interactions and armour units motions in a breakwater composed of Antifer cubes. To do so, the fluids (air and water) are simulated using an Eulerian-Eulerian CFD solver and the contacts between the blocks and the slope are solved using a DEM code. The codes were coupled and validated in a previous study, using idealised configurations that did not reflect actual coastal structures. This work extends the previous study to a semi-realistic configuration where the blocks are positioned along an inclined wall to represent the armour layer of a rubble-mound breakwater. Experiments and simulations are performed, and results are compared to evaluate the accuracy of the model. The comparisons are made on the number of displaced armour units and on their displacement amplitude. Two regular configurations are studied: a one-layer configuration and a two-layers configuration which improves the stability and better represents realistic breakwaters. The study shows that the numerical model offer a good representation of the physical phenomenon observed in the experimental campaign. Finally, simulations are performed on a randomly generated armour layer to improve the realism of the breakwater.

Accurate prediction of medium-term coastal bed level evolution via numerical modelling is essential for effective coastal management but remains computationally demanding when process-based models are forced with full wave climate datasets. Representative Morphological Wave Height (RMWH) methods offer a practical alternative by reducing wave input while preserving essential morphological principles. This study systematically revisits classical RMWH approaches and proposes three enhanced variants aimed at improving accuracy without increasing computational cost. The examined methods include: (i) the classical RMWH formulation, (ii) an energy-flux-based subdivision of directional bins, (iii) an approach accounting for interchangeable dominance of longshore and cross-shore sediment transport depending on wave incidence angle, and (iv) a variant combining RMWH with an Artificial Neural Network (ANN) to eliminate sea-states unable to initiate sediment motion.All variants were implemented using a coupled process-based numerical model to simulate annual coastal bed evolution at the port of Rethymno, Greece, and benchmarked against a brute-force simulation. Model performance was quantified using the Brier Skill Score (BSS). Results show that the proposed enhancements substantially improve predictive skill compared to the classical RMWH approach, with BSS values increasing from “Good” to “Excellent” while maintaining run-time reductions exceeding 450%. The ANN-assisted RMWH variant exhibited the best overall performance.Further validation against field bathymetric measurements from Eresos beach, Greece, and comparison with two established wave input reduction methods confirmed the robustness and efficiency of the proposed method. The findings underline that enhanced RMWH methods provide an efficient and reliable framework for medium-term coastal bed evolution modelling.

The mean wave overtopping rate is an essential parameter to design coastal protections. Estimating it with a high precision is primordial to find a balance between a satisfactory safety level and a limited impact on the environment and construction costs. A series of laboratory experiments was conducted in a wave flume to estimate the wave overtopping discharge over a rock-armored breakwater in bimodal sea state conditions (combining swell and wind waves). Both simulated swell and wind wave systems were long-crested and colinear. Preliminary tests were performed on a smooth breakwater to validate the experimental set-up. Some trends in the results with the smooth slope can be characterized by the representative wave steepness. These trends are confirmed and amplified in the presence of the armor rubble slope. In that case, the measured wave overtopping rate can be significantly overestimated by existing prediction formulas, especially for sea state conditions with a high representative wave steepness, corresponding to a high wind-wave proportion in the sea state energy. We suggest two methods to take into account the effect of sea-state bimodality via the representative wave steepness to improve the wave overtopping rate estimations for smooth and armored rubble breakwaters.

Recent studies have shown that, in coastal waters where water depth decreases significantly due to rapid bathymetric changes, the non-equilibrium dynamics (NED) substantially increases the occurrence probability of extreme (rogue) waves. Nevertheless, research on depth-induced NED has been predominantly confined to unidirectional irregular waves, while the role of directionality remains largely unexplored. The scarce studies on multidirectional waves mainly rely on numerical simulations and have yielded conflicting results. In this work, we report on an experimental investigation of wave directionality on the depth-induced non-equilibrium wave statistics. High-order statistical moments, skewness and kurtosis, are used as proxies for the non-equilibrium wave response. Our results indicate that the directional spreading has a minor effect on decreasing the maximum values of these statistical moments. In contrast, the incidence direction plays a significant role in the non-equilibrium wave response, which is attributed to the effective bottom slope.

A one-dimensional numerical model based on enhanced Serre–Green–Naghdi equations is presented and validated against a broad set of laboratory experiments of nearshore wave transformation, breaking, and run-up on slopes. The model uses a hybrid finite volume/finite difference numerical scheme with high-order MUSCL-type reconstructions, a hydrostatic reconstruction for well-balancedness and positivity of the water depth, and a third-order strong-stability-preserving Runge–Kutta time integration. Wave breaking is modelled via an eddy viscosity approach based on a depth-integrated one-equation turbulence model for the turbulent kinetic energy. The model is validated against five sets of laboratory experiments covering the shoaling, breaking, and run-up of different types of waves: solitary, regular, and irregular waves. Bed profiles with gentle or mild plane slopes, as well as steep fringing reef profiles, are considered. The validation dataset encompasses both spilling and plunging breaker types. The model demonstrates its ability to accurately reproduce not only detailed wave characteristics (wave shoaling, breaking point location, spectrum transformation, wave height decay in the surf zone, nonlinear wave shape statistics, and high-order statistical moments of the free surface elevation), but also the variations of the mean water level (wave set-down and set-up), the generation and propagation of infragravity waves, and the run-up on the beach slope.

Ejector-based cycles are widely used in heat pumps and refrigeration systems driven by low-grade heat sources, but accurate performance prediction for system control and optimization remains challenging due to the strong sensitivity of ejector behavior to operating conditions. This work introduces a novel ejector performance mapping framework based on a two-dimensional representation using the compression ratio (CR) and expansion ratio (XR), combined with a global ejector efficiency definition. The formulation enables a computationally negligible and physically interpretable reduced-order model capable of representing ejector performance. For a given ejector geometry and working fluid, the model requires calibration from a single ejector characteristic curve, allowing rapid prediction over a wide range of operating conditions. The model is developed using a CFD-generated dataset for an ammonia ejector operating under absorption-assisted heat transformer conditions and validated against independent operating points, experimental data, and state-of-the-art physics-based 0D models. Results show improved accuracy, particularly in regime-transition and single-choking conditions where conventional models exhibit larger deviations. Additional validation using literature datasets covering different working fluids, geometries, and operating conditions demonstrates the applicability of the framework following calibration for each ejector configuration.

The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the leading parameter controlling the reflection rates and types of breakers. While little is known about the effect of reflection rates on the formation of extreme nonlinear waves, some debate has arisen regarding whether high reflection rates enhance the nonlinearity at the tail of the wave height distribution through its Gram-Charlier approximation proxies (excess kurtosis and skewness). In this work, we provide theoretical evidence that at very steep beaches of smooth composition, the reflection rate nearing unity will tend to stabilize the excess kurtosis otherwise generated by shoaling and controlled in magnitude by the bottom slope magnitude. We further verified this result through fully nonlinear numerical simulations, reaching a good agreement.

Describing intricate concurrent wave processes frequently proves challenging and unwieldy. Although the influence of reflection rates on the development of extreme nonlinear waves remains poorly understood, controversy has emerged over whether elevated reflection rates amplify nonlinearity in the upper tail of the wave height distribution. Aided by fully nonlinear simulations, we present a theoretical framework that isolates the effects of shoaling length, bottom slope magnitude, and reflection rates. Comparing the simulation results with the theory for steep and reflective slopes, it is noticed that the theoretical excess kurtosis stabilizes for steep slopes with a high reflection rate, and that the simulated kurtosis remains in the confidence interval of our new theory. We therefore conclude that the high reflection rate is the main reason for anomalous wave statistics becoming stable.

The present work aims to tackle breakwater stability challenges through an innovative numerical deterministic method using a resolved DEM-CFD (Discrete Element Method-Computational Fluid Dynamics) strategy, which simulates the individual motions of armour units within a fluid solver. To achieve this, a coupling between a DEM code and a CFD code is implemented and validated. The fluids (air and water) are solved using a Eulerian-Eulerian CFD solver, and the contacts between blocks are solved using a DEM code. The solids are defined within the fluid solver using a discrete forcing approach and are therefore fully resolved. In this way, the fluid solver enables the prediction of object motions with complex shapes such as tetrapods. To couple the codes, forces exerted on the solids are calculated in the fluid solver and sent to the DEM solver. Then, contact and gravity forces are computed and added to the fluid forces. The DEM solver then computes the new positions and velocities of the bodies, which are retrieved by the fluid solver. An experimental study is performed on a fixed and instrumented idealized breakwater to evaluate the wave forces acting on a coastal structure. The experiments are then numerically reproduced to validate the numerical model. Simulations of the impact of solitary waves on a row of mobile isolated tetrapods laid on a horizontal berm are then performed using the DEM-CFD coupling. The importance of initial placement and friction parameters is investigated to show the sensitivity to these parameters.

In the coastal zone, irregular wave trains undergo strong changes due to variable water depth inducing shoaling, refraction and nonlinear wave-wave and wave-bottom interactions. Knowing the evolution of the wave spectrum and statistical distributions of free surface elevation (FSE), wave crest height and wave height is of utmost interest for many applications in coastal engineering. This includes the design of coastal and harbor structures, the prediction of morphodynamical changes and beach erosion, just to mention few of them. In this study, the whispers3D model is used to simulate the wave induced kinematics beneath regular and irregular wave trains propagating over a submerged bar. This seabed configuration provokes strong changes in the wave fields and the wave kinematics underneath resulting from the combined effects of dispersion and nonlinearity. Two wave flume experiments offering refined measurements of FSE and horizontal velocity are used to assess and quantify the accuracy of the model.

To assess the safety of coastal infrastructures against marine hazards or to design coastal or harbor protections, wave overtopping rates for extreme sea-state conditions must be estimated. A usual practice is to use empirical formulas predicting average wave overtopping discharges for a given structure profile and sea-state conditions, with the state-of-the-art being the EurOtop manual (van der Meer et al., 2018). However, the configurations for which these formulas can be applied are in limited number, simplified, and assume a uniform breakwater profile in the longshore direction. The purpose of this work is to investigate the performance of simpler numerical models for the simulation of wave overtopping over coastal structures of simple profile, namely depth-averaged weakly-dispersive wave models.

Freak waves, usually defined as waves with crest-to-trough heights exceeding twice the significant wave height Hs (e.g. Dysthe et al., 2008), pose a significant risk to maritime and ocean engineering (Didenkulova et al., 2023). These anomalous waves occur under various conditions but are particularly hazardous in coastal regions with intense human activity (Li and Chabchoub, 2023). In this study, we present experimental evidence demonstrating that, as waves propagate over an uneven bottom with the presence of uniform following current, the mean flow velocity varies according to the changes of local water depth, and the inhomogeneity of current in the direction of wave propagation leads to non-equilibrium dynamics (NED). As a result, the freak wave probability is further enhanced by a following current, which was considered the opposite in the regime of MI (Toffoli et al., 2015).

We derive and study a new family of non-local partial differential equations (PDEs) that model free-surface long gravity waves over a flat bottom. To derive the model equations we approximate the velocity potential as a series of vertical polynomials derived from the shallow-water expansion of the Dirichlet-to-Neumann problem in the Hamiltonian formulation of free-surface potential flow and invoke Luke’s variational principle. The resulting evolution equations exhibit a non-local Hamiltonian structure being coupled with a system of linear elliptic spatial PDEs on the horizontal plane. A key advantage of this approach is that it directly yields canonical Hamiltonian equations, which are well-suited for numerical solutions using standard methods. This class of model equations offers high-order shallow-water approximations of the water-wave problem. It contains terms whose spatial derivatives are at most of order two, distinguishing it from asymptotic methods involving higher-order mixed spatio-temporal derivatives. We explore the first non-trivial member of this family, highlighting its connections to other mathematical models and emphasizing its practical utility. We then analyse and discuss its linear dispersive properties and demonstrate that it does not exhibit a specific type of instability known as wave-trough instability. Additionally, we demonstrate its effectiveness in simulating the long-distance steady propagation of strongly non-linear solitary waves and the head-on collision of two counter-propagating solitary waves. In the latter case, comparisons with experimental data confirm the model’s ability to capture complex wave dynamics, including wave transformation in the presence of strong non-linearity and dispersion. The extension of this approach to accommodate variable bottom topography is briefly discussed.

The stability of armor units against wave action is a critical issue for coastal and harbor breakwaters. Most of the time, the breakwater stability is determined based on semi-empirical design formulae, as well as with experimental campaigns on scale models in wave basins. The present work aims to approach breakwater stability through a numerical deterministic approach using a DEM- CFD (Discrete Element Method – Computational Fluid Dynamics) method which simulates the individual motion of armor units inside a fluid solver. The fluid is solved using EDF Eulerian-Eulerian CFD code neptune_cfd, and the contacts between blocks are solved using the DEM code Grains3D (Wachs et al., 2012). The solids are modeled inside neptune_cfd using an IBM (Immersed Boundary Method) technique with discrete forcing.

This paper summarises the work conducted within the 1st FOWT (Floating Offshore Wind Turbine) Comparative Study organised by the EPSRC (UK) ‘Extreme loading on FOWTs under complex environmental conditions’ and ‘Collaborative computational project on wave structure interaction (CCP-WSI)’ projects. The hydrodynamic response of a FOWT support structure is simulated with a range of numerical models based on potential theory, Morison equation, Navier-Stokes solvers and hybrid methods coupling different flow solvers. A series of load cases including the static equilibrium tests, free decay tests, operational and extreme focused wave cases are considered for the UMaine VolturnUS-S semi-submersible platform, and the results from 17 contributions are analysed and compared with each other and against the experimental data from a 1:70 scale model test performed in the COAST Laboratory Ocean Basin at the University of Plymouth. It is shown that most numerical models can predict similar results for the heave response, but significant discrepancies exist in the prediction of the surge and pitch responses as well as the mooring line loads. For the extreme focused wave case, while both Navier–Stokes and potential flow base models tend to produce larger errors in terms of the root mean squared error than the operational focused wave case, the Navier-Stokes based models generally perform better. Given the fact that variations in the solutions (sometimes large) also present in the results based the same or similar numerical models, e.g., OpenFOAM, the study highlights uncertainties in setting up a numerical model for complex wave structure interaction simulations such as those involving a FOWT and therefore the importance of proper code validation and verification studies.